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Adding Subtracting Fractions

Adding Fractions

- If we were adding apples,
- 1 apple 1 apple 2 apples
- Same with fractions
- You just add the tops and copy the bottom.

Adding Fractions

- Oops!
- What if we cant just copy the bottom because

the bottoms are different?

Adding Fractions

- We need a common denominator.
- Its much easier to understand common

denominators if you understand what common

multiples are.

Multiples of a Number

- A multiple of a number is a number that you can

get by multiplying your original number by a

whole number. - For example, the multiples of 6 would be
- 6, 12, 18, 24, 30, 36, 42, 48, . . .

Common Multiples

- If you had two numbers like 6 and 12, a common

multiple would be a number that is a multiple of

each of them. - Multiples of 6 6, 12, 18, 24, . . .
- Multiples of 12 12, 24, 36, 48, . . .
- 12 and 24 are two of the many common multiples of

6 and 12.

Least Common Multiples

- Even though 6 and 12 have many common multiples,

we usually work with the smallest, or least

common multiple. - Multiples of 6 6, 12, 18, 24, . . .
- Multiples of 12 12, 24, 36, 48, . . .
- 12 is the least common multiple of 6 and 12.

Common Denominator

- In order to add or subtract fractions, you need

to have a common denominator. - The fractions must have the same number on the

bottom.

Common Denominators

- Finding common denominators is the same as

finding common multiples. - The denominator is the number on the bottom of a

fraction. - Finding a common denominator for
- is the same as finding the common multiples of 6

and 12.

Least Common Denominator

- Although you can add fractions using any common

denominator, most people like to work with

smaller numbers so they use the least common

denominator. - Its abbreviated L.C.D.

Adding Fractions

- To add these fractions, we must first transform

them into equivalent fractions that have the same

number on the bottom.

Adding Fractions

- Weve already decided that the least common

multiple of 6 and 12 is 12. - Therefore the L.C.D. of our fractions is 12.

Adding Fractions

- We only have to change the first fraction so that

it has a 12 on the bottom. - We have to be careful not to change the value of

the fraction when we change what it looks like!

Changing Fractions

- An easy way to change a 6 into a 12 is to

multiply it by 2. - If we multiply the bottom by 2, we must also

multiply the top by 2.

Changing Fractions

- Why arent we changing the value when we multiply

by 2 on the top and bottom?

Adding Fractions

- Now our problem is easy!

ARF!

- We arent finished until we reduce the answer.
- ALWAYS REDUCE FRACTIONS!

Subtracting fractions

- Good news!
- Subtracting fractions is just like adding except

that you subtract the tops and copy the bottom!

Remember

To add or subtract you need the bottoms of the

fractions to be the same.

If they arent the same, find a common

denominator. L.C.D. is the least common

denominator. Change the fraction by multiplying

the top and the bottom by the same number. Add or

subtract the tops and copy the bottom.